Reduced-Order Computational Modeling of Small UAV Acoustic Signatures and SNR-Based Passive Detection Range Using Harmonic Aeroacoustic Scaling

Small unmanned aerial vehicle (UAV) acoustic signatures are relevant to environmental noise assessment, passive monitoring, and preliminary detectability analysis. This study presents a physics-informed reduced-order framework that combines blade-passing frequency (BPF) harmonic synthesis, rotational-speed acoustic scaling, propagation, and signal-to-noise ratio (SNR) threshold crossing. The RPM–OASPL law was calibrated using ten digitized measurements for a four-rotor DJI Phantom II with Original 9450 propellers and validated, without refitting, against eleven Aftermarket 9443 measurements. The fitted exponent was m = 5.285, and the fitted reference level was Lref = 77.01 dB(A) at 5000 RPM and 1 m. A 100,000-realization Monte Carlo analysis that propagated ±100 RPM and ±0.5 dB digitization bounds, together with residual scatter, produced total 95% intervals of 5.01–5.55 for m and 76.58–77.43 dB(A) for Lref. Calibration yielded RMSE = 0.39 dB and R2 = 0.9979; independent-configuration validation yielded MAE = 2.27 dB, RMSE = 2.38 dB, and R2 = 0.9168. At 5000 RPM, nominal free-field threshold-crossing distances were 70.9, 22.4, and 7.1 m for quiet rural, semi-urban, and urban scenarios. Combined statistical 95% screening intervals were 41.3–121.7, 13.0–38.5, and 4.1–12.2 m, respectively. Sensitivity analyses show that β controls harmonic-specific range but not normalized OASPL, while ground interference, band-limited masking, and detector processing can materially change operational range. The framework is therefore a rapid, interpretable screening tool rather than a universal detector performance model.